A spatially varying differential equation for multi-patch pandemic propagation

TL;DR

This paper extends the classical SIR model to include spatial variations by deriving a nonlinear diffusion equation from discrete patches, enabling better modeling of pandemic spread across different regions.

Contribution

It introduces a novel spatially varying SIR model derived from discrete patches, incorporating nonlinear diffusion to better simulate pandemic propagation.

Findings

Derivation of a nonlinear heat flow equation for population dynamics.

Model captures spatial heterogeneity in infection and recovery.

Provides a framework for analyzing multi-patch pandemic spread.

Abstract

We develop an extension of the Susceptible-Infected-Recovery (SIR) model to account for spatial variations in population as well as infection and recovery parameters. The equations are derived by taking the continuum limit of discrete interacting patches, and results in a diffusion equation with some nonlinear terms. The resulting population dynamics can be reinterpreted as a nonlinear heat flow equation where the temperature vector captures both infected and recovered populations across multiple patches.